The bodies of 40-year-old Michael Atherton and the three women were found at the property in Greenside Avenue, Horden, near Peterlee, late on Sunday.
Three other people escaped the semi-detached house from an upstairs window, including a 19-year-old woman, who suffered minor injuries.
Police confirmed Mr Atherton was licensed to own six firearms.
Det Supt Paul Goundry, who is leading the murder inquiry – dubbed Operation Preston – said: “My preferred hypothesis is that the shootings were carried out by the 40-year-old man.”
Of all the onerous and insane gun laws in the UK, none of them stopped this. Further as far as I can tell this massacre was committed with a simple hunting shotgun.
Can we just all agree gun control doesn’t work worth a damn, and just call this whole thing off?


